CISL 2007 annual report banner

IMAGe theme for 2007: Statistics for numerical models

 
 
Model calibration technique

This figure displays contours of the posterior distribution of optimal calibration parameter values (alpha, beta, R) for the LFM model of the magnetosphere for a geomagnetic storm that occurred on January 10, 1997. A space-filling statistical design was used to choose a collection of values of the parameters (blue dots), and the resulting model runs were used to fit a statistical model to the surface representing the discrepancy between the LFM model output and satellite data from the date of the storm. The distribution of optimal calibration parameters in the figure was determined from this statistical representation of the discrepancy. The goal of this research is not only to improve the model and our understanding of the magnetosphere, but also to do so in a manner that uses computational resources most efficiently.
 
 
Model analysis with a statistical emulator

This figure displays the response of the Thermosphere-Ionosphere Electrodynamics General Circulation Model (TIE-GCM) to three parameters that describe atmospheric tides at the lower boundary (AMP and PHZ) and variations of night-time ionization rates (EDN). These figures were produced using a statistical emulator of the model, constructed from an ensemble of only 30 model evaluations. This analysis has allowed scientists working with TIE-GCM to verify the underlying code and to quantify the effects of these three parameters on the model output, and, again, to do so in a manner that uses computational resources efficiently.
 
Using statistics to compare models with observations

These figures show the results of using statistical models to capture the stochastic nature of cloud observations and to create a forcing time series to be used with a single column model (SCM) focusing on the planetary boundary layer (PBL). The figures show that the variability in wind speed (10 m above ground) and long-wave radiation emitted from the surface, as a function of time, are similar to the variability from observed clouds (solid curve). Several different statistical models are compared (colored markers). The results are also compared with the observations when very cloudy days are removed from the sample (dashed curve) showing the importance of outliers. This research is allowing scientists at NCAR to study the nature of the PBL response to clouds.
 

IMAGe's vision is to bring mathematical models and tools to bear on fundamental problems in the geosciences, and be a center of activity for the mathematical and geophysical communities. A central activity in IMAGe is the Theme-of-the-Year (TOY)—an annual focus on a particular area of the geosciences or applied mathematics—that has an impact on NCAR's scientific mission. In FY2007, the TOY focused on statistics for numerical models. Statistical science in the past 20 years has advanced to handle the interpretation of complicated multivariate, spatial and temporal data sets, and it is well suited to tackle the massive outputs from numerical experiments that are now the norm in the geosciences. The FY2007 theme was undertaken with the goal of matching cutting-edge statistical methods to the needs of geophysical model development and to make statistical scientists aware of the particular scientific issues and research in the geophysical modeling community.

This effort supports the NCAR strategic priority of "Engaging a broader and more diverse community in the atmospheric and geosciences," and it leverages three others being advanced by IMAGe: "Improving prediction of weather, climate, and other atmospheric phenomena," "Conducting computer science, computational science, applied mathematics, statistics, and numerical methods R&D," and "Developing and providing advanced services and tools."

In cooperation and collaboration with the Statistical and Applied Mathematical Sciences Institute (SAMSI) and the Mathematical Sciences Research Institute (MSRI), the main activities of the 2007 TOY were a series of three workshops and a summer graduate workshop, all held at NCAR. These TOY workshops dovetailed with SAMSI programs on random matrices and computer models and with the MSRI summer school program.

Four modeling groups at NCAR were engaged to present their models and highlight potential statistical connections at the scoping workshop in November 2006. From that starting point, several collaborations between NCAR scientists and statisticians at SAMSI and the broader statistical community were begun, and the results of these efforts were presented at a follow-up workshop in May 2007. In addition, there was a workshop in May 2007 that focused on random matrices. Finally, a summer school program on the Carbon Cycle was hosted at NCAR during July 2007.

For FY2008, the TOY will focus on geophysical turbulence. Understanding turbulent processes at a fundamental level is essential to understanding the dynamics of the atmosphere, the oceans, the planetary boundary layer, and of the sun and solar-terrestrial interactions. The 2008 TOY will emphasize the fundamental aspects of turbulence, but also team with the experimental/observational and numerical/modeling communities. A series of three workshops and a summer school are planned that will serve to promote synergy and interaction between the different communities involved.

This project is made possible through NSF Core funding. Additional funds for FY2007 were supplied by NSF's Statistical and Applied Mathematical Sciences Institute (SAMSI).